Explain How Two Samples Can Have The Same Mean

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Explain how two samples can have the same mean but different standard deviations. Draw a bar graph that shows the two samples, their means, and standard deviations as error bars.

Explanation

The mean is a measure of the center of some sample, while the standard deviation measures variation of some sample.

If two samples have the same mean, then this implies that the two values in the two samples are centered about the same value.

However, this does not mean that the data values in the samples vary the same amount about this center and thus the standard deviations can be different.

For example,

Sample 1=2,4,6,8,10

Sample 2=4,5,6,7,8

The two samples both have mean 6, because the middle values of the samples are 6 and all other data values lie symmetrically about this value.

However, the standard deviation of Sample 1 is larger than the standard deviation of Sample 2, because the data values in Sample 1 are further from center 6 than the data values in Sample 2.

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